Search the corpus

    Cardinal invariants under closed subspaces

    P-WESTOP04-06

    Area
    Topology
    Seen at
    WESLEYAN
    Years
    2004
    Status
    draft
    Contents
    1. Carefully define any three standard cardinal invariants associated with every topological space, excluding the cardinality \(|X|\) itself.
    2. For each invariant \(c\) you chose, prove or disprove: \[ F\subseteq X\text{ closed}\quad\Longrightarrow\quad c(F)\le c(X). \]
    3. For each chosen invariant, prove or disprove the same assertion under the additional hypothesis that \(X\) is metrizable.

    Solution submission

    Submit a solution on GitHub

    Source Collections